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Simplifying y2 + 60y = 5 Reorder the terms: 60y + y2 = 5 Solving 60y + y2 = 5 Solving for variable 'y'. Reorder the terms: -5 + 60y + y2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + 60y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + 60y + 5 + y2 = 0 + 5 Reorder the terms: -5 + 5 + 60y + y2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 60y + y2 = 0 + 5 60y + y2 = 0 + 5 Combine like terms: 0 + 5 = 5 60y + y2 = 5 The y term is 60y. Take half its coefficient (30). Square it (900) and add it to both sides. Add '900' to each side of the equation. 60y + 900 + y2 = 5 + 900 Reorder the terms: 900 + 60y + y2 = 5 + 900 Combine like terms: 5 + 900 = 905 900 + 60y + y2 = 905 Factor a perfect square on the left side: (y + 30)(y + 30) = 905 Calculate the square root of the right side: 30.083217913 Break this problem into two subproblems by setting (y + 30) equal to 30.083217913 and -30.083217913.Subproblem 1
y + 30 = 30.083217913 Simplifying y + 30 = 30.083217913 Reorder the terms: 30 + y = 30.083217913 Solving 30 + y = 30.083217913 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + y = 30.083217913 + -30 Combine like terms: 30 + -30 = 0 0 + y = 30.083217913 + -30 y = 30.083217913 + -30 Combine like terms: 30.083217913 + -30 = 0.083217913 y = 0.083217913 Simplifying y = 0.083217913Subproblem 2
y + 30 = -30.083217913 Simplifying y + 30 = -30.083217913 Reorder the terms: 30 + y = -30.083217913 Solving 30 + y = -30.083217913 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + y = -30.083217913 + -30 Combine like terms: 30 + -30 = 0 0 + y = -30.083217913 + -30 y = -30.083217913 + -30 Combine like terms: -30.083217913 + -30 = -60.083217913 y = -60.083217913 Simplifying y = -60.083217913Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.083217913, -60.083217913}
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